Are there Hilbert-style Pure Type Systems?

For many a natural deduction style logic there is a Hilbert-style logic that is equivalent to it in that it has the same theorems (i.e. valid judgements with empty contexts). For intuitionistic logic, the axioms of the equivalent Hilbert-style logic can be propositions which are also known as the types of the combinators I, K and S. Hilbert-style versions of illative combinatory logic have formulations with axioms that are actual type statements for I, K and S. As pure type systems (PTSs)are, in a sense, equivalent to systems of illative combinatory logic, it might be thought that Hilbert-style PTSs (HPTSs) could be based in a similar way. This paper shows that some PTSs have very trivial equivalent HPTSs, with only the axioms as theorems and that for many PTSs no equivalent HPTS can exist. Most commonly used PTSs belong to these two classes. For some PTSs however, including lambda* and the PTS at the basis of the proof assistant Coq, there is a nontrivial equivalent HPTS, with axioms that are type statements for I, K and S.Comment: Accepted in Logical Methods in Computer Scienc

On a possibility to determine the S-factor of the hep process in experiments with thermal (cold) neutrons

The problem of the magnitude of the S--factor of the hep process $p + {^3\mathrm{He}} \to {^4\mathrm{He}} + e^+ + \nu_e$ is one of the most important unsolved problems in nuclear astrophysics. The magnitude of $S(hep)$ has also an important impact on the interpretation of the Super-Kamiokande solar neutrino results in terms of neutrino oscillations. We point out the possiblity to determine the major hadronic contribution to $S(hep)$ from the measurement of the total cross section of the process $n + {^3\mathrm{H}} \to {^4\mathrm{He}} + e^- + \bar{\nu}_e$ in experiments with high intensity beams of thermal or cold neutrons.Comment: 7 pages, revtex, no figures; note added; final version to be published in Astropart. Phy

Final-state interactions in inclusive deep-inelastic scattering from the deuteron

We explore the role of final-state interactions (FSI) in inclusive deep-inelastic scattering from the deuteron. Relating the inclusive cross section to the deuteron forward virtual Compton scattering amplitude, a general formula for the FSI contribution is derived in the generalized eikonal approximation, utilizing the diffractive nature of the effective hadron-nucleon interaction. The calculation uses a factorized model with a basis of three resonances with mass $W<2$ GeV and a continuum contribution for larger $W$ as the relevant set of effective hadron states entering the final-state interaction amplitude. The results show sizeable on-shell FSI contributions for Bjorken $x \gtrsim 0.6$ and $Q^2 \lesssim 10$ GeV$^2$, increasing in magnitude for lower $Q^2$, but vanishing in the high-$Q^2$ limit due to phase space constraints. The off-shell rescattering contributes at $x \gtrsim 0.8$ and is taken as an uncertainty on the on-shell result.Comment: 29 pages, 8 figures. Version accepted for publication in PRC. Minor changes: some discussion in the introduction is slightly expanded (three typos in formulas corrected

Oxidation-resistant coatings for refractory metals used in inert atmospheres

Test conditions and results are reported for various coatings on a 1 percent zirconium columbium alloy at a temperature of 2000 deg F. Molybdenum silicide over molybdenum is most effective coating, tin-aluminum coating is adequately protective, chromium-molybdenum silicides are not protective

Plastic bags in evacuated chamber make lightweight gas sampling system

Portable, lightweight system collects the exhaust gas of an aircraft during flight for use in analyzing combustion efficiency. The system uses an evacuated chamber and plastic bags

Increasing efficiency of switching type regulator circuits Patent

Switching series regulator with gating control networ

Thermal treatment and mechanical properties of aluminum-2021

Mechanical properties, after thermal treatments, are summarized for sheet and plate of copper-rich, high-strength, heat-treatable aluminum-2021. The alloy is quench sensitive, quench rate and variations in aging affect corrosion behavior. Aging effects on yield strength, tensile strength, and elongation of sheet and plate are compared